Simplify the following expression: $ r = \dfrac{-1}{10} - \dfrac{y + 6}{y - 8} $
Solution: In order to subtract expressions, they must have a common denominator. Multiply the first expression by $\dfrac{y - 8}{y - 8}$ $ \dfrac{-1}{10} \times \dfrac{y - 8}{y - 8} = \dfrac{-y + 8}{10y - 80} $ Multiply the second expression by $\dfrac{10}{10}$ $ \dfrac{y + 6}{y - 8} \times \dfrac{10}{10} = \dfrac{10y + 60}{10y - 80} $ Therefore $ r = \dfrac{-y + 8}{10y - 80} - \dfrac{10y + 60}{10y - 80} $ Now the expressions have the same denominator we can simply subtract the numerators: $r = \dfrac{-y + 8 - (10y + 60) }{10y - 80} $ Distribute the negative sign: $r = \dfrac{-y + 8 - 10y - 60}{10y - 80}$ $r = \dfrac{-11y - 52}{10y - 80}$